We present a parallel multithreaded incomplete Cholesky-conjugate gradient (ICCG) solver for a linear system derived from a finite element electromagnetic field analysis. Algebraic block multicolor ordering is introduced to parallelize the solver with a high cache hit ratio and convergence comparable to the sequential solver. We develop the parallel ICCG solver based on reordering with modification for electromagnetic field analyses involving external circuits. The numerical results from practical models show that a 2.6- to 3.8-fold speedup compared with the sequential solver is attained using eight cores.